A subcompact car, mass 1,000 kg, runs into and sticks to an at-rest, 2,200 kg SUV. lf their final speed is 4.7 m/s, what was the smaller car's initial speed?

1 Answer
Feb 21, 2018

15.04 m/s

Explanation:

First, because of the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

p_(sc) = initial momentum of the subcompact car
note that the initial momentum of the SUV is 0 because it is at rest.
p_(suv)' = final momentum of the SUV
p_(sc)' = final momentum of the subcompact car.
also note that the final velocities of the cars are the same so that will be denoted as v'

p_(sc) = p_(sc)' + p_(suv)'
(m_(sc))(v_(sc)) = (m_(sc))(v')+(m_(suv))(v')

solve for v_(sc)

v_(sc)= ((m_(sc))(v')+(m_(suv))(v'))/(m_(sc))

plug in numbers

v_(sc) = (1000*4.7+2200*4.7)/1000
v_(sc) = 15.04 m/s